You are to design a roller coaster in which cars start from rest at a height h=3

Question

You are to design a roller coaster in which cars start from rest at a height h=30m, roll down into a valley, and then up a mountain. Fig:

a) What is the speed of the cars at the bottom of the valley?

B) if the passengers are to feel 8G at the bottom of the valley, what must be the radius R of the arc of circle that fits the bottom of the valley?

C) the top of the next mountain is an arc of circle of the same radius R. If the passengers are to feel 0G at the top of this mountain, what must be its height h'?

Please explain a, b, and c .....

Explanation / Answer

a) mv^2/2 = mgh, so v = sqrt(2gh) = 24.2 m/s

b) 8G - G = mv^2/R, 7Rg = v^2, 7Rg = 2gh, so R =2h/7 = 8.57 m

c) speed at top = u, mu^2/2 = mgh - mgh', so u^2 = 2g(h - h')

G = mu^2/R, so mu^2 = mgR, u^2 = gR

then 2g(h-h') = gR

h - h' = R/2 = h//7

h'= 6h/7 = 25.7 m

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